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In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: *''Group'' with a partial function replacing the binary operation; *''Category'' in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation, called ''inverse'' by analogy with group theory. Notice that a groupoid where there is only one object is a usual group. Special cases include: *''Setoids'', that is: sets that come with an equivalence relation; *''G-sets'', sets equipped with an action of a group ''G''. Groupoids are often used to reason about geometrical objects such as manifolds. introduced groupoids implicitly via Brandt semigroups.〔(Brandt semigroup ) in Springer Encyclopaedia of Mathematics - ISBN 1-4020-0609-8〕 == Definitions == A groupoid is an algebraic structure (G,) consisting of a non-empty set G and a binary partial function '' defined on G. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「groupoid」の詳細全文を読む スポンサード リンク
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